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Input-to-state stability for parabolic boundary control: Linear and semi-linear systemsAug 22 2019Input-to-state stability (ISS) for systems described by partial differential equations has seen intensified research activity recently, and in particular the class of boundary control systems, for which truly infinite-dimensional effects enter the situation. ... More
A Nonseparable Invariant Extension of Lebesgue Measure -- A Generalized and Abstract ApproachAug 22 2019Here using some methods of combinatorial set theory, particularly the ones related to the construction of independent families of sets and some modified version of the notion of small sets originally introduced by Riecan, Riecan and Neubrunn, we give ... More
Brown Measures of Free Circular and Multiplicative Brownian Motions with Probabilistic Initial PointAug 22 2019Given a selfadjoint random variable $x_0$ and a unitary random variable $u$, different from Haar unitary, free from the free circular Brownian motion $c_t$ and the free multiplicative Brownian motion $b_t$, we use the Hamilton-Jacobi method to compute ... More
The polarization constant of finite dimensional complex spaces is oneAug 21 2019The polarization constant of a Banach space $X$ is defined as $$\mathbf c(X):= \limsup\limits_{k\rightarrow \infty} \mathbf c(k, X)^\frac{1}{k},$$ where $\mathbf c(k, X)$ stands for the best constant $C>0$ such that $ \Vert \overset{\vee}{P} \Vert \leq ... More
Analog for the Wiener Lemma for Wolff-Denjoy SeriesAug 21 2019Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the function 1/f, then the remaining fractional part of this function will also ... More
Constrained convex bodies with extremal affine surface areasAug 21 2019Given a convex body K in R^n and p in R, we introduce and study the extremal inner and outer affine surface areas IS_p(K) = sup_{K'\subseteq K} (as_p(K') ) and os_p(K)=inf_{K'\supseteq K} (as_p(K') ), where as_p(K') denotes the L_p-affine surface area ... More
Complete boundedness of multiple operator integralsAug 21 2019In this paper, we characterize the multiple operator integrals mappings which are bounded on the Haagerup tensor product of spaces of compact operators. We show that such maps are automatically completely bounded and prove that this is equivalent to a ... More
Quasi-local Algebras and Asymptotic ExpandersAug 21 2019In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a discrete metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic ... More
On the Banach lattice c_0Aug 21 2019We show that $c_0$ is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. On the other hand, we show that $c_0$ is complemented in the free Banach lattice generated by itself (seen as a Banach space). As a consequence, ... More
Algebra of convolution type operators with continuous data on Banach function spacesAug 21 2019We show that if the Hardy-Littlewood maximal operator is bounded on a reflexive Banach function space $X(\mathbb{R})$ and on its associate space $X'(\mathbb{R})$, then the space $X(\mathbb{R})$ has an unconditional wavelet basis. As a consequence of the ... More
A $C^m$ Lusin Approximation Theorem for Horizontal Curves in the Heisenberg GroupAug 20 2019We prove a $C^m$ Lusin approximation theorem for horizontal curves in the Heisenberg group. This states that every absolutely continuous horizontal curve whose horizontal velocity is $m-1$ times $L^1$ differentiable almost everywhere coincides with a ... More
Multilinear operator-valued Calderón-Zygmund theoryAug 20 2019We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition naturally arising ... More
On coupled best proximity points and Ulam-Hyers stabilityAug 20 2019For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a uniformly convex Banach space $X$ consider a mapping $T:(A \times B) \cup (B \times A) \rightarrow A \cup B$ satisfying $T(A,B) \subset B$ and $T(B, A) \subset A$. In this paper the ... More
Operators which are polynomially isometric to a normal operatorAug 19 2019Aug 21 2019Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on $\mathcal{B}(\mathcal{H})$ and two linear ... More
Normal operators with highly incompatible off-diagonal cornersAug 19 2019Let $\mathcal{H}$ be a complex, separable Hilbert space, and $\mathcal{B}(\mathcal{H})$ denote the set of all bounded linear operators on $\mathcal{H}$. Given an orthogonal projection $P \in \mathcal{B}(\mathcal{H})$ and an operator $D \in \mathcal{B}(\mathcal{H})$, ... More
Dyadic norm Besov-type spaces as trace spaces on regular treesAug 19 2019In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.
The fractional porous medium equation on manifolds with conical singularitiesAug 19 2019We show $R$-sectoriality for the fractional powers of possibly non-invertible $R$-sectorial operators. Applications concern existence, uniqueness and maximal $L^{q}$-regularity results for solutions of the fractional porous medium equation on manifolds ... More
On Two Families of Funk-Type TransformsAug 19 2019We consider two families of Funk-type transforms that assign to a function on the unit sphere the integrals of that function over spherical sections by planes of fixed dimension. Transforms of the first kind are generated by planes passing through a fixed ... More
Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin SpacesAug 19 2019We use Bochner's subordination technique to obtain caloric smoothing estimates in Besov- and Triebel--Lizorkin spaces. Our new estimates extend known smoothing results for the Gau{\ss}--Weierstra{\ss}, Cauchy--Poisson and higher-order generalized Gau{\ss}--Weierstra{\ss} ... More
Rates of convergence for iterative solutions of equations involving set-valued accretive operatorsAug 19 2019This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract explicit rates ... More
Computing Spectral Measures and Spectral Types: New Algorithms and ClassificationsAug 19 2019Despite new results on computing the spectrum, there has been no general method able to compute spectral measures (as given by the classical spectral theorem) of infinite-dimensional normal operators. Given a matrix representation, we show that if each ... More
On the Hypercyclicity Criterion for operators of Read's typeAug 19 2019Let $T$ be a so-called operator of Read's type on a (real or complex) separable Banach space, having no non-trivial invariant subset. We prove in this note that $T\oplus T$ is then hypercyclic, i.e. that $T$ satisfies the Hypercyclicity Criterion.
On the ${\Ext}^2$-problem for Hilbert spacesAug 18 2019We show that $\Ext^2(\ell_2, \ell_2)\neq 0$ in the category of Banach spaces. This solves a sharpened version of Palamodov's problem and provides a solution to the second order version of Palais problem. We also show that $\Ext^2(\ell_1, \K)\neq 0$ in ... More
Homological dimensions of Banach spacesAug 18 2019The purpose of this paper is to lay the foundations for the study of the problem of when $\Ext^n(X, Y)=0$ in Banach/quasi-Banach spaces. We provide a number of examples of couples $X,Y$ so that $\Ext^n(X,Y)$ is (or is not ) $0$, including the first example ... More
Riesz means in Hardy spaces on Dirichlet groupsAug 18 2019Given a frequency $\lambda=(\lambda_n)$, we study when almost all vertical limits of a $\mathcal{H}_1$-Dirichlet series $\sum a_n e^{-\lambda_ns}$ are Riesz-summable almost everywhere on the imaginary axis. Equivalently, this means to investigate almost ... More
Bifurcation for Minimal Surface Equation in Hyperbolic $3$-ManifoldsAug 18 2019Initiated by the work of Uhlenbeck in late 1970s, we study questions about the existence, multiplicity and asymptotic behavior for minimal immersions of closed surface in some hyperbolic three-manifold, with prescribed conformal structure on the surface ... More
On Orlicz-Jensen-Hermite-Hadamard inequalities and their applications in Convex GeometryAug 18 2019In this paper we show some Orlicz-Jensen-Hermite-Hadamard inequality and a reverse to that inequality. This establishes, in particular, one of the first multidimensional Hermite-Hadamard inequality in this generality. We then show several consequences ... More
Reduction principle for a certain class of kernel-type operatorsAug 17 2019The classical Hardy--Littlewood inequality asserts that the integral of a product of two functions is always majorized by that of their non-increasing rearrangements. One of the pivotal applications of this result is the fact that the boundedness of an ... More
Ultraholomorphic extension theorems in the mixed settingAug 16 2019The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results have already been ... More
Exponential integrability in the spirit of Moser-Trudinger's inequalities of functions with finite non-local, non-convex energyAug 16 2019Let $d \ge 1$, $p \ge d$, and let $\Omega$ be a smooth bounded open subset of $\mathbb{R}^d$. We prove some exponential integrability in the spirit of Moser-Trudinger's inequalities for measurable functions $u$ defined in $\Omega$ such that $$ \mathop{\int_{\Omega} ... More
Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noiseAug 16 2019In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination of suitable bootstrap-type arguments and a detailed analysis of the ... More
A Theorem of Roe and Strichartz on homogeneous treesAug 16 2019In 1980, J. Roe proved that if $\{f_{k}\}_{k\in\mathbb{Z}}$ is doubly infinite sequence of functions in $\mathbb{R}$ which is uniformly bounded and satisfies $(df_{k}/dx)=f_{k+1}$ for all $k\in\mathbb{Z}$ then $f_{0}(x)=a\sin(x+\theta)$ for some $a,\theta\in\mathbb{R}$. ... More
An entire free holomorphic function which is unbounded on the row ballAug 16 2019We give an entire free holomorphic function $f$ which is unbounded on the row ball. That is, we give a holomorphic free noncommutative function which is continuous in the free topology developed by Agler and McCarthy but is unbounded on the set of row ... More
Iterative Neural Networks with Bounded WeightsAug 16 2019A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these results, we show ... More
Iterative Neural Networks with Bounded WeightsAug 16 2019Aug 19 2019A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these results, we show ... More
Noncommutative partial convexity via $Γ$-convexityAug 16 2019Motivated by classical notions of partial convexity, biconvexity, and bilinear matrix inequalities, we investigate the theory of free sets that are defined by (low degree) noncommutative matrix polynomials with constrained terms. Given a tuple of symmetric ... More
Regularization of linear ill-posed problems involving multiplication operatorsAug 16 2019We study regularization of ill-posed equations involving multiplication operators when the multiplier function is positive almost everywhere and zero is an accumulation point of the range of this function. Such equations naturally arise from equations ... More
Higher Rank Numerical Ranges of Jordan-Like MatricesAug 15 2019We completely characterize the higher rank numerical range of the matrices of the form $J_n(\alpha)\oplus\beta I_m$, where $J_n(\alpha)$ is the $n\times n$ Jordan block with eigenvalue $\alpha$. Our characterization allows us to obtain concrete examples ... More
An Improved Compact Embedding Theorem for Degenerate Sobolev SpacesAug 15 2019This short note investigates the compact embedding of degenerate matrix weighted Sobolev spaces into weighted Lebesgue spaces. The Sobolev spaces explored are defined as the abstract completion of Lipschitz functions in a bounded domain $\Omega$ with ... More
Frequently dense harmonic functions and universal martingales on treesAug 15 2019Aug 17 2019We prove the existence of harmonic functions $f$ on trees, with respect to suitable transient transition operators $P$, that satisfy an analogue of Menshov universal property in the following sense: $f$ is the Poisson transform of a martingale on the ... More
Frequently dense harmonic functions and universal martingales on treesAug 15 2019We prove the existence of harmonic functions f on trees, with respect to suitable transient transition operators P, that satisfy an analogue of Menshov universal property in the following sense: f is the Poisson transform of a martingale on the boundary ... More
Additive Local Multiplications and zero-preserving maps on $C(X)$Aug 15 2019Suppose $X$ is a compact Hausdorff space. In terms of topolocical properties of $X$, we find topological conditions on $X$ that are equivalent to each of the following: 1. every additive local multiplication on $C\left( X\right) $ is a multiplication, ... More
Moments of the weighted Cantor measuresAug 14 2019Based on the seminal work of Hutchinson, we investigate properties of {\em $\alpha$-weighted Cantor measures} whose support is a fractal contained in the unit interval. Here, $\alpha$ is a vector of nonnegative weights summing to $1$, and the corresponding ... More
Some Gruss type inequalities for Frechet differentiable mappingsAug 14 2019Let X be a Hilbert C^*-module on C^*-algebra A and p in A. We denote by Dp(A;X) the set of all continuous functions f on A, which are Frechet differentiable on a open neighborhood U of p. Then, we introduce some generalized semi-inner products on Dp(A;X), ... More
Operator inequalities I. Models and ergodicityAug 14 2019We discuss when an operator, subject to an inequality in heridatary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. To the contrary to the previous work, the kernel ... More
On Expansive MappingsAug 14 2019When finding an original proof to a known result describing expansive mappings on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to total boundedness preserves the isometry property and nearly so that ... More
A Tauberian theorem for ideal statistical convergenceAug 13 2019Given an ideal $\mathcal{I}$ on the positive integers, a real sequence $(x_n)$ is said to be $\mathcal{I}$-statistically convergent to $\ell$ provided that $$ \textstyle \left\{n \in \mathbf{N}: \frac{1}{n}|\{k \le n: x_k \notin U\}| \ge \varepsilon\right\} ... More
Time-changed Dirac-Fokker-Planck equations on the latticeAug 13 2019A time-changed discretization for the Dirac equation is proposed. More precisely, we consider a Dirac equation with discrete space and continuous time perturbed by a time-dependent diffusion term $\sigma^2Ht^{2H-1}$ that resembles to a latticizing version ... More
Projecting onto Helson matrices in Schatten classesAug 13 2019A Helson matrix is an infinite matrix $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on the product $mn$. We demonstrate that the orthogonal projection from the Hilbert--Schmidt class $\mathcal{S}_2$ onto the subspace of Hilbert--Schmidt ... More
Numerical radius inequalities for linear operators and operator matricesAug 13 2019We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. We also obtain some upper and lower bounds for the numerical radius of operator matrices ... More
Quantitative combinatorial geometry for concave functionsAug 12 2019We prove several exact quantitative versions of Helly's and Tverberg's theorems, which guarantee that a finite family of convex sets in $R^d$ has a large intersection. Our results characterize conditions that are sufficient for the intersection of a family ... More
Positivity Certificates via Integral RepresentationsAug 12 2019Complete monotonicity is a strong positivity property for real-valued functions on convex cones. It is certified by the kernel of the inverse Laplace transform. We study this for negative powers of hyperbolic polynomials. Here the certificate is the Riesz ... More
The $\partial$-complex on weighted Bergman spaces on Hermitian manifoldsAug 12 2019In this paper, we generalize several results about the $\partial$-complex on the Segal-Bargmann space of $\mathbb{C}^n$ to weighted Bergman spaces on Hermitian manifolds. We also study in detail the $\partial$-complex on the unit ball with the complex ... More
Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groupsAug 12 2019We prove an almost everywhere convergence result for Bochner-Riesz means of $L^p$ functions on Heisenberg-type groups, yielding the existence of a $p>2$ for which convergence holds for means of arbitrarily small order. The proof hinges on a reduction ... More
Extremal functions for a singular Hardy-Moser-Trudinger inequalityAug 12 2019In this paper, using blow-up analysis, we prove a singular Hardy-Morser-Trudinger inequality, and find its extremal functions. Our results extend those of Wang-Ye (Adv. Math. 2012), Yang-Zhu ( Ann. Glob. Anal. Geom. 2016), Csat\'{o}- Roy (Calc. Var. 2015), ... More
Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equationsAug 11 2019In this paper strong dissipativity of generalized time-fractional derivatives on Gelfand triples of properly in time weighted $L^p$-path spaces is proved. In particular, the classical Caputo derivative is included as a special case. As a consequence one ... More
Bisynchronous Games and Factorizable MapsAug 11 2019We introduce a new class of non-local games, and corresponding densities, which we call bisynchronous. Bisynchronous games are a subclass of synchronous games and exhibit many interesting symmetries when the algebra of the game is considered. We develop ... More
Wavelet transforms associated with the Index Whittaker transformAug 10 2019Aug 16 2019In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as reconstruction ... More
Wavelet transforms associated with the Index Whittaker transformAug 10 2019In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as reconstruction ... More
Fractional operators via analytic interpolation of integer powersAug 09 2019Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct non-integer powers of ... More
The angle along a curve and range-kernel complementarityAug 09 2019In this paper, we define the angle of a bounded linear operator $A$ along an unbounded path emanating from the origin and use it to characterize range-kernel complementarity. In particular we show that if $0$ faces the unbounded component of the resolvent ... More
On convergent sequences in dual groupsAug 09 2019We provide some characterizations of precompact abelian groups $G$ whose dual group $G_p^\wedge$ endowed with the pointwise convergence topology on elements of $G$ contains a nontrivial convergent sequence. In the special case of precompact abelian \emph{torsion} ... More
Large number of bubble solutions for a perturbed fractional Laplacian equationAug 09 2019This paper deals with the following nonlinear perturbed fractional Laplacian equation $$(-\Delta)^s u = K(|y'|,y'')u^{\frac{N+2s}{N-2s}\pm\epsilon},\,\,u>0,\,\,u\in D^{1,s}(\mathbb{R}^N),$$ where $0<s<1, N\geq 4,$ $(y',y'')\in \mathbb{R}^2\times \mathbb{R}^{N-2},$ ... More
Embeddings of homogeneous Sobolev spaces on the entire spaceAug 09 2019We completely characterize the validity of the inequality $\|u\|_{Y(\mathbb{R}^n)}\leq C \|\nabla^m u\|_{X(\mathbb{R}^n)}$, where $X$ and $Y$ are rearrangement-invariant spaces, by reducing it to a considerably simpler one-dimensional inequality. Furthermore, ... More
On existence and uniqueness properties for solutions of stochastic fixed point equationsAug 09 2019The Feynman-Kac formula implies that every suitable classical solution of a semilinear Kolmogorov partial differential equation (PDE) is also a solution of a certain stochastic fixed point equation (SFPE). In this article we study such and related SFPEs. ... More
On Function Spaces with Mixed Norms --- A SurveyAug 09 2019The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed Morrey ... More
A generalization of order convergenceAug 08 2019Let $E$ be a sublattice of a vector lattice $F$. $\left( x_\alpha \right)\subseteq E$ is said to be $ F $-order convergent to a vector $ x $ (in symbols $ x_\alpha \xrightarrow{Fo} x $), whenever there exists another net $ \left(y_\alpha\right) $ in $F ... More
Unbounded $σ$-order-to-norm continuous and $un$-continuous operatorsAug 08 2019An operator $T $ from a vector lattice $E$ into a normed lattice $F$ is called unbounded $\sigma$-order-to-norm continuous whenever $x_{n}\xrightarrow{uo}0$ implies $\| Tx_{n}\|\rightarrow 0$, for each sequence $(x_{n})_n\subseteq E$. For a net $(x_{\alpha})_{\alpha}\subseteq ... More
Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded belowAug 08 2019Given a complete, connected Riemannian manifold $ \mathbb{M}^n $ with Ricci curvature bounded from below, we discuss the stability of the solutions of a porous medium-type equation with respect to the 2-Wasserstein distance. We produce (sharp) stability ... More
The Periodic Dilation Completeness Problem: Cyclic vectors in the Hardy space over the infinite-dimensional polydiskAug 08 2019The classical completeness problem raised by Beurling and independently by Wintner asks for which $\psi\in L^2(0,1)$, the dilation system $\{\psi(kx):k=1,2,\cdots\}$ is complete in $L^2(0,1)$, where $\psi$ is identified with its extension to an odd $2$-periodic ... More
Some homogeneous $q$-difference operators and the associated generalized Hahn polynomialsAug 08 2019In this paper, we first construct the homogeneous $q$-shift operator $\widetilde{E}(a,b;D_{q})$ and the homogeneous $q$-difference operator $\widetilde{L}(a,b; \theta_{xy})$. We then apply these operators in order to represent and investigate generalized ... More
3D Compton scattering imaging: study of the spectrum and contour reconstructionAug 08 20193D Compton scattering imaging is an upcoming concept focusing on exploiting the photons scattered, following on from the so-called Compton effect, by the atomic structure of an object under study. This phenomenon rules the collision of particles with ... More
Balian-Low type theorems on homogeneous groupsAug 08 2019We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let $N$ be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let $(\pi, \mathcal{H}_{\pi})$ ... More
Korovkin-type results on convergence of sequences of positive linear maps on function spacesAug 08 2019In this paper we deal with the convergence of sequences of positive linear maps to a (not assumed to be linear) isometry on spaces of continuous functions. We obtain generalizations of known Korovkin-type results and provide several illustrative examples. ... More
Equations of the first kind and the inversion of series of resolvents of a closed operatorAug 08 2019Aug 16 2019Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (\alpha_j -A)^{-1}$ are given. Several examples are considered.
Equations of the first kind and the inversion of series of resolvents of a closed operatorAug 08 2019Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (\alpha_j -A)^{-1}$ are given. Several examples are considered.
Two remarks on the interpolation spaceAug 08 2019Dans ce travail, on montre que $(M(\mathbb{T}),c_0(\mathbb{Z}))_\theta = (L^1,c_0(\mathbb{Z}))_\theta$, $0<\theta <1$. Dans la suite on montre pour le couple d'interpolation $(C_0,C_1)$ trouv\'e par Garling-Smith qu'il existe un isomorphisme $U_\theta: ... More
Two remarks on the interpolation spaceAug 08 2019Aug 14 2019Dans ce travail, on montre que $(M(\mathbb{T}),c_0(\mathbb{Z}))_\theta = (L^1,c_0(\mathbb{Z}))_\theta$, $0<\theta <1$. Dans la suite on montre pour le couple d'interpolation $(C_0,C_1)$ trouv\'e par Garling-Smith qu'il existe un isomorphisme $U_\theta: ... More
Wall-to-wall optimal transportAug 08 2019Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of velocity fields by a P\'eclet number $\text{Pe}$ proportional to their root-mean-square ... More
Wall-to-wall optimal transport in two dimensionsAug 08 2019Aug 20 2019Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of velocity fields by a P\'eclet number $\text{Pe}$ proportional to their root-mean-square ... More
A Structure Theorem for Isometries on Discrete Variable-Exponent Lebesgue SpacesAug 07 2019We investigate the structure of norm-preserving linear operators on variable-exponent, discrete Lebesgue spaces. A certain class of isometries, novel to this work, are especially considered; this class completely coincides with all isometries when the ... More
Biangular Gabor frames and Zauner's conjectureAug 07 2019Two decades ago, Zauner conjectured that for every dimension $d$, there exists an equiangular tight frame consisting of $d^2$ vectors in $\mathbb{C}^d$. Most progress to date explicitly constructs the promised frame in various dimensions, and it now appears ... More
Sobolev type spaces associated with the Poly-axially operatorAug 07 2019In this paper n-dimensional Sobolev type spaces $ E_{\alpha}^{s,p}(\R^n_+)$ $(\alpha\in \R^n,\;\;\alpha_1> -\frac{1}{2},...,\alpha_n>-\frac{1}{2}, s\in \R, p\in [1,+\infty])$ are defined on $\R^n_+$ by using Fourier-Bessel transform. Some properties including ... More
Spectrum is rational in dimension oneAug 07 2019A bounded measurable set $\Omega\subset{\mathbb R}^d$ is called a spectral set if it admits some exponential orthonormal basis $\{e^{2\pi i \langle\lambda,x\rangle}: \lambda\in\Lambda\}$ for $L^2(\Omega)$. In this paper, we show that in dimension one ... More
A non-nuclear $C^*$-algebra with the Weak Expectation Property and the Local Lifting PropertyAug 07 2019We construct a non-exact $C^*$-algebra $A$ with both the Weak Expectation Property (WEP) and the Local Lifting Property (LLP). This gives a new example of non-nuclear $A$ for which there is a unique $C^*$-norm on $A \otimes A^{op}$. This example is of ... More
On maximal multiplicities for Hamiltonians with separable variablesAug 07 2019For $\mathbb N^*:=\mathbb N \setminus \{0\}$, we consider the collection $\mathfrak M(N)$ of all the $N$ rows, for which, for $n=1,\cdots,N$, the $n-th$ row consists of an increasing sequence $(a_j^n)_j$ of real numbers. For $\mathfrak A \in \mathfrak ... More
Two Applications of Boolean Valued AnalysisAug 07 2019The paper contains two main results that are obtained by Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector sublattices that are ... More
Open embeddings and pseudoflat epimorphismsAug 06 2019We characterize open embeddings of Stein spaces and of $C^\infty$-manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras.
Limit operators techniques on general metric measure spaces of bounded geometryAug 06 2019We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit operators, characterizations ... More
On the non-hypercyclicity of normal operators, their exponentials, and symmetric operatorsAug 06 2019Aug 08 2019We give a simple straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which, under a certain ... More
On the non-hypercyclicity of normal operators, their exponentials, and symmetric operatorsAug 06 2019We give a simple straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which, under a certain ... More
Real-Variable Characterizations of Local Hardy Spaces on Spaces of Homogeneous TypeAug 06 2019Suppose that $(X,d,\mu)$ is a space of homogeneous type, with upper dimension $\mu$, in the sense of R. R. Coifman and G. Weiss. Let $\eta$ be the H\"{o}lder regularity index of wavelets constructed by P. Auscher and T. Hyt\"{o}nen. In this article, the ... More
Plurisubharmonic Noncommutative Rational FunctionsAug 05 2019A noncommutative (nc) function in $x_1,\dots,x_g,x_1^*,\dots,x_g$ is called plurisubharmonic (plush) if its nc complex Hessian takes only positive semidefinite values on an nc neighborhood of 0. The main result of this paper shows that an nc rational ... More
Generalized Fourier--Feynman transforms and generalized convolution products on Wiener space IIAug 05 2019The purpose of this article is to present the second type fundamental relationship between the generalized Fourier--Feynman transform and the generalized convolution product on Wiener space. The relationships in this article are also natural extensions ... More
Factorizations of Schur functionsAug 05 2019The Schur class, denoted by $\mathcal{S}(\mathbb{D})$, is the set of all functions analytic and bounded by one in modulus in the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$, that is \[ \mathcal{S}(\mathbb{D}) = \{\varphi \in H^\infty(\mathbb{D}): ... More
Some Remarks on Diametral Dimension and Approximate Diametral Dimension of Certain Nuclear Fréchet SpacesAug 05 2019The diametral dimension, $\Delta(E)$, and the approximate diametral dimension, $\delta (E)$, of a nuclear Fr\'echet space $E$ which satisfies $\underline{DN}$ and $\Omega$, is related to power series spaces $\Lambda_{1}(\varepsilon)$ and $\Lambda_{\infty}\left(\varepsilon\right)$ ... More
Symmetric shift-invariant subspaces and harmonic mapsAug 05 2019The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class ... More
The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifoldsAug 05 2019Aug 18 2019We introduce a quasi-convex relaxation of the $\mathsf{CD}(K,N)$ condition we call the Quasi Curvature-Dimension condition $\mathsf{QCD}(Q,K,N)$. Our motivation stems from a recent interpolation inequality along Wasserstein geodesics in the ideal sub-Riemannian ... More
The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifoldsAug 05 2019We introduce a quasi-convex relaxation of the $\mathsf{CD}(K,N)$ condition we call the Quasi Curvature-Dimension condition $\mathsf{QCD}(Q,K,N)$. Our motivation stems from a recent interpolation inequality along Wasserstein geodesics in the ideal sub-Riemannian ... More
The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifoldsAug 05 2019Aug 07 2019We introduce a quasi-convex relaxation of the $\mathsf{CD}(K,N)$ condition we call the Quasi Curvature-Dimension condition $\mathsf{QCD}(Q,K,N)$. Our motivation stems from a recent interpolation inequality along Wasserstein geodesics in the ideal sub-Riemannian ... More